Precise measurements of the gap energy of folded acoustic phonons in Si/${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Ge}}_{\mathit{x}}$ superlattices

We report high-resolution Raman measurements of the gap widths of folded longitudinal-acoustic phonons in Si/${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Ge}}_{\mathit{x}}$ superlattices. The first four gap widths at the minizone boundary were studied systematically. It was found that to fit the measured gap widths by Rytov theory one has to use a reduced sound velocity and density from that of bulk Si for the Si layers and a higher sound velocity and density of the alloy layers than the value deduced by linear interpolation. In the high-resolution measurements fine structure of the phonon peaks was observed together with a linewidth narrowing when approaching the minizone boundary. The variation of the scattering intensities recorded at different wavelengths and for several orders of folding provides an opportunity for a precise test of light scattering theory near the minizone boundary.